Kinetic Roughening in Slow Combustion of Paper

Maunuksela, J.; Myllys, Markko; Kähkönen, O.-P.; Timonen, J.; Provatas, Nikolas; Alava, Mikko J.; Ala-Nissilä, Tapio

doi:10.1103/physrevlett.79.1515

Cited by 111 publications

(120 citation statements)

References 18 publications

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“…The equipment we use in slow-combustion experiments has been described elsewhere [4,5], so it suffices to say here that samples were 'burned' in a chamber with controllable conditions and that the video signal of propagating fronts was compressed and stored on-line on a computer. The spatial resolution of the set up was 120 µm, and the time resolution was 0.1 s. For the samples we used the lens-paper grade (Whatman) we have used also previously [5].…”

Section: Methodsmentioning

confidence: 99%

“…As slow-combustion fronts do not propagate in paper without adding an oxygen source for maintaining the chemical reaction involved, we added as before [4,5] a small amount of potassium nitrate in the samples. This method also allows for a relatively easy way to produce advancing and retarding columnar defects.…”

Section: Methodsmentioning

confidence: 99%

“…Recent experiments on slow-combustion fronts propagating in paper [4,5], and on flux fronts penetrating a high-T c thin-film superconductor [6], have provided new insight into this problem [7]. It indeed appears that short-range-correlated noise, quenched and dynamical, with possibly at the same time a non-Gaussian amplitude distribution for small time differences, induce an additional time and an additional length scale, beyond which KPZ scaling can only be observed.…”

Section: Introductionmentioning

confidence: 99%

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Effect of a columnar defect on the shape of slow-combustion fronts

et al. 2003

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We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with excess or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for excess vs. reduced driving in the defect, clearly demonstrates the existence of a KPZ-type of nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough excess driving, and that there is a corresponding increase then in the average front speed. This increase in the average front speed disappears at a non-zero excess driving in agreement with the simulated behavior of the ASEP model.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of a columnar defect on the shape of slow-combustion fronts

et al. 2003

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“…This is clearly illustrated nowadays by the large variety of studies dealing with front invasion where roughening processes take place such as flow through porous media [16][17][18] or imbibition [19], flame propagation [20,21], deposition processes [14,15], and flux penetration in superconducting materials [32,33,45,46]. From a macroscopic point of view, the development of modeling techniques for the description of these dynamical systems has been generally based on the traditional approach to transport phenomena, where the governing expressions are usually differential equations representing local balances of the quantity of interest (e.g., mass, momentum, flux of superconducting vortices, etc.)…”

Section: Gradient Driven Dynamics: Front Invasionmentioning

confidence: 99%

Deblocking of interacting particle assemblies: from pinning to jamming

Miguel¹,

Andrade²,

Zapperi³

2003

Braz. J. Phys.

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A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.

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“…Complementary experimental work was scant, but provocative-see early, comprehensive reviews [28,29,30]. This epoch closed with the beginnings of Finnish investigations [31] of kinetically-roughened KPZ firelines, key mathematical papers [32,33], as well as refreshing nonperturbative [34] and conformally invariant [35] perspectives, the former inspiring numerical rebuttals [36,37,38,39] of a stubborn, battered suggestion [40], revived nevertheless shortly thereafter [41], that 4+1 might be the upper critical dimension (UCD) of the KPZ problem. Recent numerics [42,43,44,45] appear to have buried this idea, but from the analytical side [46,47], there's lingering suspicion that something nontrivial is afoot near this particular dimension.…”

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confidence: 99%

A KPZ Cocktail-Shaken, not Stirred...

2015

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The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we i) pay debts to heroic predecessors, ii) highlight additional, experimentally relevant aspects of the recently solved 1+1 KPZ problem, iii) use an expanding substrates formalism to gain access to the 3d radial KPZ equation and, lastly, iv) examining extremal paths on disordered hierarchical lattices, set our gaze upon the fate of d=∞ KPZ. Clearly, there remains ample unexplored territory within the realm of KPZ and, for the hearty, much work to be done, especially in higher dimensions, where numerical and renormalization group methods are providing a deeper understanding of this iconic equation.Keywords Nonequilibrium Growth · Extremal Paths · Universal Limit Distributions In a NutshellThe history of physics has been punctuated at seminal moments by the appearance of certain fundamental equations (and associated models) which have vigorously propelled the enterprise forward, serving as an explosively rich departure point, generating a myriad of alternative perspectives, creative insights, surprising connections and, given its sustained impregnability, often remain for many years a sacred object of fascination and obsession to its dedicated disciples. Recent, obvious suspects in this regard include the quantum mechanical Schrödinger equation (equally well, its flipside-Feynman's path integral formulation), or the wonderfully elusive Navier-Stokes equation governing fluid mechanics, by which may be gleaned the scaling secrets of turbulent flow, dynamically encoded in the whirling eddies drawn by da Vinci centuries ago. Within the domain of equilibrium statistical physics, the 2d Ising Model, with its tour-de-force algebraic solution by Onsager, followed by combinatoric, graphical, Grassmannian, Monte Carlo, as well as full-blown field-theoretic, scaling, and renormalization group treatments, represents an extraordinary legacy that continues unabated to this very day. Arguably, a non-equilibrium statistical mechanical analogue to Ising/Onsager is the iconic equation [1] proposed a generation ago by Kardar, Parisi, and Zhang (KPZ); it captures the statistical fluctuations of a kinetically-roughened scalar height field h(x, t):

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Kinetic Roughening in Slow Combustion of Paper

Cited by 111 publications

References 18 publications

Effect of a columnar defect on the shape of slow-combustion fronts

Effect of a columnar defect on the shape of slow-combustion fronts

Deblocking of interacting particle assemblies: from pinning to jamming

A KPZ Cocktail-Shaken, not Stirred...

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